The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  2  1  2  1  1  1  1  1  1  1  X  1  2  1  1  0  1  1  0  1  1  1  1  X  1  0  1  1  1  1  1  2  2  1  X  X  X  1  X  1  1
 0  X  0  0  0  0  0  2  2  X X+2  X  X  X X+2  X  0 X+2  2  X  2  X  0  X  2 X+2  X  0 X+2  2 X+2  0  0  2  0  X  X X+2  2  2 X+2  0  0  2 X+2  X  X  0  X  2  0  X X+2 X+2  0  X X+2  2  2  0  0 X+2  2  0  X X+2  2  2  2 X+2  2 X+2  0  0  0 X+2  X  X  0  2  X  2  2  X  X  0
 0  0  X  0  0  2 X+2  X  X  X  X  X X+2  0  0  0  2  2 X+2  X  2  0  0 X+2  2  2  X X+2  0  X  X X+2  X X+2 X+2  0  2  0  0  2 X+2  2  X  X  X  2  X  0  2  0  0 X+2  0  X  2  2  2  X X+2  X  0 X+2  X  X  2  X X+2  0 X+2  0  2 X+2  0  X  X  X  2  X X+2  0  X  2  X X+2  2  0
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  0  X  X  2  X  2 X+2  0 X+2  0  2  X  2  X  X  2  X  X  0  0  2  X  0 X+2  2 X+2  X  2  0  0  X  0 X+2  2 X+2  X  X  X  2  0  2  2  0  2  0  0  2  0  2 X+2  X  X  2 X+2  0 X+2  0  X  X  X  X  0  X  X  X  2  X  0  2 X+2  0  0  2  0
 0  0  0  0  X  X  2 X+2  X X+2  2  2  X  2 X+2  X  X  2  2 X+2  0 X+2  0 X+2 X+2 X+2  0 X+2  0  X  0  2  0 X+2  X  0  2 X+2 X+2  0 X+2 X+2  0  2 X+2 X+2  0 X+2  0  0  2  2 X+2  2  X  X  2  X  0  2  X  0  0 X+2 X+2  X  X X+2  X  X X+2 X+2 X+2  X X+2  0  0  2  0  X X+2  0  2 X+2  X  0

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+32x^78+72x^79+102x^80+138x^81+157x^82+154x^83+141x^84+174x^85+187x^86+192x^87+193x^88+140x^89+79x^90+60x^91+47x^92+38x^93+40x^94+18x^95+20x^96+14x^97+16x^98+14x^99+8x^100+8x^101+2x^103+1x^142

The gray image is a code over GF(2) with n=344, k=11 and d=156.
This code was found by Heurico 1.16 in 0.734 seconds.